Question

Ann-Marie is comparing costs at two locations for an event. Location 1 charges $100 per hour and $20 per person. Location 2 charges a flat fee of $600 for up to 25 guests. For what number of guests,

g
, will Location 2 be less expensive, if her event lasts 4 hours and she has less than 25 guests?

Answer 1

We must have less than 10 guests

Explanation:

Location 1

cost = 100h+20p where h = hours and p = person

Location 2

cost = 600 for p < 25

Since there are less than 25 guests and h = 4 both equations are valid

Location 1

cost = 100(4)+20p = 400+20p

Location 2

cost = 600

We want location 2 to be less expensive

600< 400+20p

Subtract 400 from each side

600-400 < 20p

200 <20p

Divide by 20

200/20 < 20p/20

10 <p

We must have less than 10 guests